Reasoning About Collectively Accepted Group Beliefs

A proof-theoretical treatment of collectively accepted group beliefs is presented through a multi-agent sequent system for an axiomatization of the logic of acceptance. The system is based on a labelled sequent calculus for propositional multi-agent epistemic logic with labels that correspond to possible worlds and a notation for internalized accessibility relations between worlds. The system is contraction-and cut-free. Extensions of the basic system are considered, in particular with rules that allow the possibility of operative members or legislators. Completeness with respect to the underlying Kripke semantics follows from a general direct and uniform argument for labelled sequent calculi extended with mathematical rules for frame properties. As an example of the use of the calculus we present an analysis of the discursive dilemma.